Minimization of a quasi-concave function over an efficient set. (English) Zbl 0799.90100

The author investigates the nonconvex optimization problem of minimizing a quasiconcave function on the set of efficient points of a linear vector minimization problem. Since all efficient vertices of the polytope given by the linear problem are not known in general, a cutting plane algorithm is presented which can be used for the determination of an approximate solution of this problem in a finite number of steps. It is also shown that this algorithm performs better, if the objective function is linear.
Reviewer: J.Jahn (Erlangen)


90C29 Multi-objective and goal programming
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming


Full Text: DOI


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